A polynomial modeling and state feedback control of blood glucose regulatory in diabetic patients

In this paper a new linear state feedback controller for artificial pancreas is proposed to regulate the blood glucose level in diabetic patients. Diabetes mellitus is a family of chronic metabolic diseases in which body´s blood glucose regulatory system doesn´t function properly. In this study, Bergman´s minimal model has been used as a base model, to reformulate dynamics of insulin and glucose concentrations in blood´s plasma as a constrained polynomial dynamical system. Since it is hard to derive exact value of parameters in most biological systems, all parameters of the model has been considered uncertain and therefore parametric uncertainty has been exploited in control design. Based on sum of squares technique, a linear state feedback controller has been obtained to regulate the blood´s insulin and glucose concentration levels around the basal levels. Main achievements of this paper are simplicity of controller structure which makes it easy to implement, parametric uncertainty to cover more patients and patient-nonspecific design, and employment of nonlinear techniques without any simplifications.